Tarina kuulostaa uskomattomalta.

Because after kuulostaa (to sound), Finnish usually uses an adjective or noun in the ablative case.

So:

• uskomaton = the basic dictionary form, incredible / unbelievable
• uskomattomalta = the form used after kuulostaa

This pattern is very common:

• Se kuulostaa hyvältä. = It sounds good.
• Tuo kuulostaa pahalta. = That sounds bad.
• Tarina kuulostaa uskomattomalta. = The story sounds unbelievable.

Even though -lta/-ltä often has a literal meaning like from, after verbs like kuulostaa it is just the normal grammatical pattern.

The dictionary form is uskomaton.

Here is the chain:

• uskoa = to believe
• uskomaton = unbelievable / incredible
• uskomattomalta = ablative singular form of uskomaton

The stem changes a little when endings are added:

• uskomaton
• stem: uskomattoma-
• ablative ending: -lta
• result: uskomattomalta

This kind of change is normal for many -ton / -tön adjectives.

No.

• kuulla = to hear
• kuulostaa = to sound

Examples:

• Kuulen musiikkia. = I hear music.
• Musiikki kuulostaa hyvältä. = The music sounds good.

So in your sentence, kuulostaa does not mean that someone is hearing the story. It describes the impression the story gives: it sounds unbelievable.

Because tarina is the subject of the sentence.

In Finnish, the subject is very often in the nominative singular basic form when it is a singular countable noun.

So:

• tarina = the story / a story
• Tarina kuulostaa uskomattomalta. = The story sounds unbelievable.

The verb agrees with it:

• tarina = singular
• kuulostaa = 3rd person singular

Finnish has no articles like English a/an and the.

So tarina can mean:

• a story
• the story

Which one is meant depends on context.

In a real conversation, the listener would understand from the situation whether it means a story in general or the story already being discussed.

Yes, but it means something slightly different.

• Tarina kuulostaa uskomattomalta. = The story sounds unbelievable.
• Tarina on uskomaton. = The story is unbelievable.

So:

• kuulostaa gives an impression based on what you have heard
• on states it more directly as a fact or judgment

English works the same way:

• It sounds unbelievable is softer or more tentative
• It is unbelievable is stronger and more direct

Because the subject tarina is singular.

Finnish verbs agree with the subject in person and number.

Present tense of kuulostaa:

• minä kuulostan
• sinä kuulostat
• hän kuulostaa
• me kuulostamme
• te kuulostatte
• he kuulostavat

Since tarina is singular and third person, the correct form is kuulostaa.

If the subject were plural:

• Tarinat kuulostavat uskomattomilta. = The stories sound unbelievable.

Here kuulostaa works like a linking verb, similar to English sound, seem, or feel.

It does not take a direct object in this sentence. Instead, it links the subject to a description.

Structure:

• Tarina = subject
• kuulostaa = linking verb
• uskomattomalta = predicative complement in the ablative

So this is not like I hear the story. It is more like The story sounds unbelievable.

Yes. Finnish word order is fairly flexible, although the neutral order here is:

• Tarina kuulostaa uskomattomalta.

You could also say:

• Uskomattomalta tarina kuulostaa.

That puts more emphasis on uskomattomalta.

Or:

• Kuulostaa uskomattomalta, tuo tarina.

That can sound more conversational or emphatic.

But for learners, the basic order subject + verb + complement is the safest and most natural starting point.

Because the basic pattern after kuulostaa is simply the ablative form of the adjective:

• hyvältä
• oudolta
• mahdottomalta
• uskomattomalta

Forms like -ltaan / -ltään can exist in other structures, but they are not what you need here. In this sentence, plain uskomattomalta is exactly right.

The ending -lta / -ltä is the usual ablative ending in singular.

Because of vowel harmony:

• back vowels → -lta
• front vowels → -ltä

Since uskomaton contains back vowels (u, o, a), the ending is -lta, not -ltä.

Compare:

• hyvä → hyvältä
• outo → oudolta
• uskomaton → uskomattomalta

Yes. It is very useful to memorize kuulostaa + ablative as a fixed pattern.

Some very common examples:

• kuulostaa hyvältä = sound good
• kuulostaa pahalta = sound bad
• kuulostaa oudolta = sound strange
• kuulostaa tutulta = sound familiar
• kuulostaa uskomattomalta = sound unbelievable

If you learn the whole pattern instead of trying to build it from scratch every time, Finnish will feel much easier.